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AlekseyPX
2 years ago
13

Philip ran out of time while taking a multiple-choice test and plans to guess the last 4 questions. Each question has 5 possible

choices, one of which is correct. Let X=X=X, equal the number of answers Philip correctly guesses in the last 444 questions. Assume that the results of his guesses are independent.
What is the probability that he answers exactly 1 question correctly in the last 4 questions?
Mathematics
1 answer:
White raven [17]2 years ago
8 0

Using the binomial distribution, it is found that there is a 0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

Considering that there are 4 questions, and each has 5 choices, the parameters are given as follows:

n = 4, p = 1/5 = 0.2.

The probability that he answers exactly 1 question correctly in the last 4 questions is P(X = 1), hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{4,1}.(0.2)^{1}.(0.8)^{3} = 0.4096

0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

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WITCHER [35]

Part (a)

The domain is the set of allowed x inputs of a function.

The graph shows that x = 0 is not allowed because of the vertical asymptote located here. It seems like any other x value is fine though.

<h3>Domain: set of all real numbers but x \ne 0</h3>

To write this in interval notation, we can say (-\infty, 0) \cup (0, \infty) which is the result of poking a hole at 0 on the real number line.

--------------

The range deals with the y values. The graph makes it seem like it stretches on forever in both up and down directions. If this is the case, then the range is the set of all real numbers.

<h3>Range: Set of all real numbers</h3>

In interval notation, we would say (-\infty, \infty) which is almost identical to the interval notation of the domain, except this time of course we aren't poking at hole at 0.

=======================================================

Part (b)

<h3>The x intercepts are x = -4 and x = 4</h3>

We can compact that to the notation x = \pm 4

These are the locations where the blue hyperbolic curve crosses the x axis.

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Part (c)

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=======================================================

Part (d)

The vertical asymptote is located at x = 0, so the equation of the vertical asymptote is naturally x = 0. Every point on the vertical dashed line has an x coordinate of zero. The y coordinate can be anything you want.

<h3>Answer: x = 0 is the vertical asymptote</h3>

=======================================================

Part (e)

The oblique or slant asymptote is the diagonal dashed line.

It goes through (0,0) and (2,6)

The equation of the line through those points is y = 3x

If you were to zoom out on the graph (if possible), then you should notice the branches of the hyperbola stretch forever upward but they slowly should approach the "fencing" that is y = 3x. The same goes for the vertical asymptote as well of course.

<h3>Answer:  Oblique asymptote is y = 3x</h3>
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sdas [7]
Simplifies to:
1.690196x+396.139706=2

Let's solve your equation step-by-step.
1.690196x+396.139706=2


Step 1: Subtract 396.139706 from both sides.

1.690196x+396.139706-396.139706=2-396.139706



1.690196x=-394.139706

Step 2: Divide both sides by 1.690196.
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x= -233.191716
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